A stack of oranges is compactly arranged so the bottom layer consists of
oranes in an equilateral triangle with n oranges on a side. The layer
next to the bottom consists of n-1 oranges on a side. This pattern
continues upward with one orange on the top. How many oranges are there?

A woman walks 10 steps down on a downward-moving escalator to reach the
bottom. As she reaches the bottom, she runs back up the same escalator at
a speed 5 times that which she walked down, covering 25 steps in reaching
the top. How many steps are visible on the escalator when it is still?

I'm trying to guess a 4-digit number with unique digits and after each
guess I'm told how many digits are correct and in the right place and
how many are correct but in the wrong place. I use that feedback to
make better and better guesses until I find the correct number. Is
there a general strategy to minimize the guesses needed?

For numbers A, B, C, and D, subtract A from B, (or vice-versa; you
must be left with a whole number, not a negative one). Repeat with
B and C, C and D, and D and A. After about 6 steps, you will always
end up with 0000. The puzzle is to get as many steps as possible.

A cafe sold tea at 30 cents a cup and cakes at 50 cents each. Everyone
in a group had the same number of cups of tea and the same number of
cakes. The bill came to $13.30. How many cups of tea did each person
have?

A piece of plywood has three holes it it: a circular hole with a
diameter of 2 cm, a square hole with 2 cm sides, and a triangular hole
with a base and height of 2 cm. What object could completely plug AND
pass completely through each hole?

If multiple small equilateral triangles are drawn within a larger one,
what is the relation between the number of small triangles lying on the
base of the big triangle and the total number contained within the big
triangle?